Effects of Kinesthetic and Concrete–Pictorial–Abstract Instruction on Grade 10 Students' Mathematical Problem-Solving Skills

This study examined the effectiveness of the Kinesthetic and Concrete–Pictorial–Abstract (CPA) instructional approaches in enhancing the mathematical problem-solving skills of Grade 10 students. Guided by Kolb's Experiential Learning Theory, Bruner's Theory of Representation, and Polya's four-step problem-solving framework, the study employed a quantitative quasi-experimental non-equivalent comparison group design involving 62 Grade 10 students from Ilayang Yuni Junior and Senior Integrated National High School, Mulanay, Quezon, Philippines. Two intact class sections were purposively selected based on dominant learning styles and were exposed to a crossover intervention in which one group received the Kinesthetic approach followed by the CPA approach, while the other group received the interventions in reverse order. A researcher-developed mathematical problem-solving test on permutations and combinations, validated by experts and scored using an adapted Polya-based rubric, served as the primary instrument. Data were analyzed using descriptive statistics, repeated-measures analysis of variance, and post hoc comparisons at the 0.05 significance level. Findings revealed that both instructional approaches significantly improved students' mathematical problem-solving skills across the four dimensions of understanding the problem, devising a plan, carrying out the plan, and reflecting on the solution. Students demonstrated the greatest gains in carrying out the plan and devising a plan, while reflecting on the solution remained the least developed dimension despite significant improvement. The crossover implementation further indicated that both approaches complemented one another, with the CPA approach strengthening conceptual understanding and procedural fluency, and the Kinesthetic approach enhancing engagement and reflective thinking. The findings suggest that integrating multisensory and representation-based instructional approaches can substantially improve mathematical problem-solving competencies and provide an effective pedagogical framework for secondary mathematics instruction.